Chapter 2
aggregation. This process is usually referred to as slow aggregation.
For fast aggregation, if it is Brownian diffusion dominated, the process is
referred to as perikinetic aggregation and the rate of change of the number of
droplets per unit volume N is given by[18]:
- ʃ = kpN2 = (8^)7V2 = (⅛2, W) = --~⅞- [2.13]
dt 3η 1 + kpNtJ
Here D is the diffusion coefficient of the droplets, η is the viscosity of the
continuous phase and N0 is the initial number concentration Ofdroplets in solution.
If non-Brownian forces dominant the displacement of the droplets,
aggregation is termed as Orthokinetic[18]. In this case, the rate is:
-^ = 4„№=(|л’С)№, N(I) = ʌ''1 [2.14]
at 3 1 + k0N0t
Here G is the velocity gradient, ко is the Orthokinetic rate constant. At room
temperature, perikinetic aggregation would be more significant for smaller
particles (R < 2 μm) and Orthokinetic aggregation would dominate otherwise (R >
5 μm).
For slow aggregation, the rate is [19]:
_dN_=k^Ni [2.15]
dt W
Here kp is the perikinetic rate and И/is the so-called stability ratio.
19